Rather than attempt to digest the arguments of the article, I will point out why any redefinition is misleading. The article also argues that Bank of England accounting is archaic and stupid. Given that following archaic and stupid rules is a core part of Britain’s brand, I see no need to argue against such a claim. My interest is with central bank balance sheets more generally.
The earlier iteration of my arguments are found on page 93 of Abolish Money (From Economics)! (https://books2read.com/abolishmoney). This book is a collection of my rants about how people discuss money, and is an excellent Christmas gift for your friends (or enemies).
The Correct Answer
Central banks in free-floating (“fiat”) currencies are special. We need to understand why that is. Rather than start with the wrong answer (the monetary line items on the central bank balance sheet), I will start with the correct answer (the way central banks operate).
We arrive at the conclusions in three steps.
Negative equity (insolvency) only matters if the entity is illiquid — unable to meet current obligations.
Central banks of free-floating currency sovereigns cannot become illiquid.
Therefore, negative equity (insolvency) does not matter for such central banks.
(Any familiarity with online Modern Monetary Theory (MMT) wrangling leaves us with a couple of extensions. The first is that since the central bank is a subsidiary of the fiscal arm of government in modern democracies, central bank operations are the core reason why currency sovereigns do not face involuntary bankruptcy. The second is the definition of “currency sovereign” is somewhat fuzzy in the real world, and is tested by “Can this sovereign really be forced into bankruptcy?”)
In other words, it is a fundamental mistake to look at particular items on the balance sheet and claim they are the secret sauce to central bank power. Instead, the secret sauce is how they operate. This is a very close analogy to the mistake that Monetarists make: that the measured quantity of money in the economy has some form of analytical magic associated with it, when the reality is that the magic comes from transactions being denominated in the unit of account defined by monetary instruments.
Before we go any further, I will cover some basics.
Assets, Liabilities, Equity, and Capital
One of the useful properties of balance sheets is that they balance. At all times, the relationship:
Assets = Liabilities + (Owner’s Equity)
holds.
Assets are what an entity owns. The value of assets on a balance sheet is typically the (depreciated) purchase price of the asset, although all assets need to be reviewed by accountants to see if their balance sheet carrying value can be justified.
Liabilities are what a company owes. Although it appears that many people use “liability” and “debt” interchangeably, this is not proper accounting practice. Debts are a class of financial instruments that meet certain tests, and not all obligated future payments meet those tests.
Owner’s Equity is the residual of (Assets - Liabilities), and tells us what the entity is worth to the common equity owners if the entity was liquidated at balance sheet values (a big valuation if).
Preferred shares are a hybrid — they look like liabilities from a cash flow perspective, but they are seen to be part of a firms “permanent capital.” (Capital is a term that is thrown around, but has a variety of meanings. I will discuss bank capital below.) Classical preferred shares are perpetual instruments (consols) that have a fixed payment. The reason why they end up classified as equity is that payments on them are optional in the sense that missed payments do not qualify the holders the right to force the issuer into bankruptcy, rather there are penalties (defined in the offering prospectus) that typically end up with the preferred shares being converted into equity (at rates disadvantageous to current common equity holders).1
If we put aside preferreds, the owner’s equity part of the balance sheet operates differently than liabilities. Although owner’s equity can rise/fall as the result of direct transfers between the firm and the owners (capital infusions/dividends, respectively), owner’s equity rises and falls every time there is a profitable/loss-making transaction. Other liabilities (and preferred shares) categories on the balance sheet only rise and fall in response to transactions that affect those instruments in particular.
The Life and Death of Banknotes
I will have to look into the exact mechanisms of the distribution of banknotes for my banking manuscript. But for my purposes, I just need to note that I see the transactions as not being charity transactions. The central bank does not give away banknotes to the private banks (and any other entity in the banknote distribution business) nor are the returns of old banknotes a charitable donation by the private sector. Banknotes are sold to/from the central bank, with the counter-party ultimately paying for the banknotes via a payment on some wholesale payments system (or via settlement balance change at the central bank, which is economically equivalent).
And note that these transactions occur effectively on demand by private sector banks — if they were unable to dump old banknotes on the central bank, they would refuse taking them, and banknotes would suddenly lose their value. This would be a default by the central bank on its customary obligations, and there would be a rather lot of angry voters that are party to the bankruptcy event.
Bank Capital
There are a variety of definitions of bank capital — new ones appear as soon as the old ones are discredited. Bank capital consists of owner’s equity plus various categories of instruments that are supposed to absorb credit losses ahead of depositors and other senior creditors: preferred shares, subordinated debt, conditional debts, etc. The theory is that the owners of bank capital instruments can get stuffed while the bank can continue operating normally.
Since debt instruments make their way into “bank capital,” we see it is a fuzzy category.
Can We Move Banknotes on Central Banks’ Balance Sheets?
We now turn to the question as to whether we can move banknotes from the nasty and dirty category of “liabilities” to some other category that has more positive vibes? Let us examine the possibilities.
Assets? Lol, lmao. Assets need to be owned by the entity, and they have to economic value. A central bank does not own banknotes in somebody else’s pocket, nor does it have any way to sell them. They might get a warm, fuzzy feeling that they are greasing the wheels of commerce with money issuance, but the carrying value for warm, fuzzy feelings is nil. More importantly, moving them from Liabilities to Assets would mean that the balance sheet equation Assets = Liabilities + (Owner’s Equity) would no longer balance.
Owner’s Equity? No, since they do not confer ownership of the central bank, nor rise and fall with profits and losses. Attempting to do this also has the side effect that central bank’s selling banknotes is pure profits and buying them is a pure loss — since the other side of the transaction is a transfer in the payments system, which is valued at par. This creates phantom profits and losses for exchanges at fair value for the central bank, even though its counterparty is engaging in a profit-neutral trade. This breaks accounting identities economy wide — which needs to be fixed by adding a “change in banknotes” plug into every equation involving aggregate income.
Some new category that does not currently exist in accounting? I.e., central banks have Assets = Liabilities + (Banknotes) + (Owner’s Equity). There is nothing stopping someone from doing that, but nobody is going to take it seriously since this new category behaves identically to any other class of liabilities. The accounting profession is not going to recall every single accounting textbook to add a new balance sheet category that has one entry on one entity’s balance sheet.
Move off the balance sheet entirely? This is impossible, since balance sheets would no longer balance. We cannot shrink Assets to match the drop in Liabilities, since none of the assets are impaired. The only way to get the balance sheet to balance is to stuff the entry into Owner’s Equity, which does not work.
Move them to “Equity” like preferred shares? (Equity being Owner’s Equity plus preferreds). This is the only viable option, and nobody other than people who believe that money is magic would take it seriously. Preferreds are perpetual instruments, while banknotes are redeemed on demand.
Bank Capital? The reason why we cannot reclassify banknotes as “bank capital” on the balance sheet (under the accounting conventions that I am familiar with) is that “bank capital” is a footnote. That is, it is a quantity that only matters for regulatory purposes, and is presented seperately.
So we are stuck with either a meaningless change (“banknotes aren’t liabilities, they are a new category that exists nowhere else in accounting”) or ideological zealots attempt to bludgeon accountants into accepting that instruments that may be redeemed on demand are the same thing as perpetual instruments whose payments may be deferred or even eliminated entirely (at the cost of equity conversion).
One side issue in the Bholat article is the notion of “expected returns.” Should banknotes get special treatment because they have a 0% expected return? This might have looked interesting in a world where interest rates are always positive, but our New Keynesian central banker friends destroyed any meaning attached to the 0% interest rate. An instrument paying 0% might eventually have a higher return than government bonds, and we can no longer use expected returns as a meaningful accounting test.
Banknotes are Not Perpetual
I have seen arguments to the effect that banknote (or money) issuance is a perpetual form of finance for the government. One looks at the balance sheet entry, and it grows forever.
This is not true, and this should be obvious to anyone familiar with European practices. Entire banknote issuances are routinely withdrawn from circulation. The pound notes I had from a trip to the U.K. in 2013 were withdrawn by the time I returned in 2023, and the only way to redeem them was to open a bank account or possibly visit the Bank of England. (I gave them to my sister-in-law.) Although some banknotes do disappear from circulation (lost or collected), the expectation at issue is that any banknote will be returned to the source at any time.
Ever-expanding balance sheets are not a sign that liabilities are not redeemed. If we look at almost any issuer of bonds that jumped from investment grade to default quickly, the bonds issued line item was most likely growing right up until default.
A Simple Thought Experiment
We need only look at a simple thought experiment to see why banknotes are indeed liabilities. There is no economic constraint that stops the Bank of Canada from loading up its fleet of B-52s and carpet bombing Canadian city centres with $10 quadrillion in new Canadian $20 bills. (I assume that there legal constraints against this policy, but laws can be changed by Parliament, while economic constraints cannot.)
The outcome of such a policy would be disastrous — everybody would rush to spend them as cash, and stuff them into private banks so that they can use them in electronic payments. The value of the Canadian dollar would disappear in a puff of hyperinflation.
It is easy to see why this is the case if banknotes are a liability of the Bank of Canada: it added $10 quadrillion in new liabilities, and no new assets. This implies that the BoC took a $10 quadrillion loss to its balance sheet. This loss is what created the $10 quadrillion gain in private sector balance sheets that fuels the hyperinflation.
But if we try to re-classify banknotes to something more benign or drop them from the a balance sheet, we see the problem immediately.
If off balance sheet, the $10 quadrillion issue has literally no effect, and so it offers no explanation why the economy went pear-shaped.
If we put banknotes as Owner’s Equity, we run into a conundrum — owner’s equity allegedly increased, but assets did not. So we get a phantom loss of $10 quadrillion that matches the alleged capital infusion, and so the balance sheet is unchanged. So why did the economy blow up?
If we pretend that banknotes are equivalent to preferred shares, how is it possible that people are redeeming them via shipping them back to banks (who then ship them to the central bank)?
Dan Rohde responded to my argument on Bluesky by arguing that central banks do not operate this way — banknotes are only created on demand. However, this is only because central bankers know that banknotes are economically equivalent to liabilities.
Concluding Remarks
Central banks are privileged by how they operate. Understanding their privileges requires looking at the operation of the entire monetary system. Pestering accountants with novel theories because you do not like the sound of the word “liability” is not going to help that understanding.
Appendix: Do Central Bank Profits Matter?
One of the problems with progressives’ revolt against the terminology of “sound finance” is that they tend to take too rosy a view of government finances. I think it would be fairly easy to find arguments on the internet that profits and losses by the central bank do not matter, since the central bank is needed to further the public purpose.
Unfortunately, the “public purpose” collides with the ugly reality that central banks need to trade with unwashed and venal fixed income market participants. Trading is a zero-sum activity (cash flows from instruments make fixed income markets positive sum).
A central bank trading loss is somebody else’s trading gain. If the central bank manages to lose money, it has done something stupid that has transferred income to some actors in the private sector — either bondholders or banks. Does it serve the private purpose for unelected bureaucrats to transfer income to those people (with almost no useful oversight from elected officials)?
At this point, I can imagine some comments to the effect that monetary payments do not matter coming from online MMT activists that have not paid much attention to what the theory actually says. Although monetary transfers are not the same thing as real resource transfers, there is an inflation constraint. Transfers to one group represent an opportunity cost limiting transfers to another group. As such, even if the dollar amounts may not be the best guide to policy, central bank losses do matter.
Tax authorities (in the U.S., possibly elsewhere) made the distinction squishier. The payments made on preferred shares are considered dividends and not interest payments under tax law, and thus not an expense (which reduces taxes paid). The authorities decided that long-dated bond issuance was a way to issue pseudo-preferreds as instruments that had interest deductions. They decided to reclassify such debts into preferreds for tax purposes.
Personally, when I read, “monetary issue is good for the economy, so how can it be a liability?” my first thought was this person doesn’t know ANYTHING about what they are talking about. Send them back to accounting 101 with instructions to take at least the next level above that (201?) before they even want to think out loud about such concepts.
ReplyDeleteThe analogy I try to use with people is that debt/liabilities come in many forms. Just like beer does… there are ales, lagers, stouts, IPAs, witbier, etc… Government liabilities are like that… you’ve got your bonds, notes, perpetual bonds, etc… and in this grouping is currency! It’s effectively a zero-coupon bond that pays no interest. It is a liability of the central government… and since the central bank is basically a subsidiary of the central government it must be held by the central bank in such a fashion that the movement of those funds between those two entities nets out correctly.
I typically try to also throw in a comment about one’s mortgage being an asset to the bank even thought they record it as a debt/liability on their balance sheet. If you realize that the banks balance sheet doesn’t look and operate like yours, why would you assume the government’s looks and operate like yours.
As a funny fact I do believe the consolidated US government balance sheet technically holds coinage as equity on its balance sheet. They at least have it on the correct side of the ledger even if it is miscategorized. I’d suspect it ended up there from some similar crazy, heated debate where one side was definitely deficient in their understanding of basic accounting.
This all got me thinking, but I believe at the basic visual accounting level in the US the FED holds currency as an asset on its balance sheet. That said, the FED does not create coin or currency it acquires the needed item from the US Mint (coins) or the US Bureau of Engraving and Printing (paper currency) which are also agents/subsidiaries of the US Treasury. So, from an accounting perspective even if coin & currency is held as an asset at the FED, no NET new coin and currency can be created without an offsetting debt/liability (or equity, in stupid but not impossible accounting arrangements). In the US case, at a consolidated level, it will be with the US Treasury – per current operational requirements that will have to show an increase in liabilities to offset the rise in the FED’s asset acquisition of net new currency. So even in the end where you place “currency” in the category of asset there must be a counter right side liability (or a dumb forced equity entry) even if that entry is not labeled “currency”.
DeleteCurrency in circulation shows up with other liabilities in the "factors reducing reserves in circulation" (which is how they present their weekly balance sheets). *Treasury* currency does show up as an asset, but that's a small entry, and is not what people are referring to in this debate - banknotes in circulation.
DeleteFrom the Flow of Funds, we see the entry:
Monetary authority; currency outside banks; liability
https://www.federalreserve.gov/releases/z1/20241212/html/l109.htm
(I missed the notification about your comment, sorry.)
DeleteGreat post, Brian! Thanks.
ReplyDeleteGood to see someone defend the accounting. It's amazing how educated and well-read people like Bholat (and Eric Lonergan, in some previous discussions) can show such ignorance towards accounting logic. Perhaps a sign that monetary theory is not where it should be?
You make some interesting observations regarding liabilities vs. equity. Would you protest if I suggested that dividing the RHS of the B/S into liabilities + equity is a shareholder's perspective, and that from a more general perspective (of the accountant) those two could be lumped together (assets=liabilities, or at least debits=credits)?
I like to keep it simple. On the LHS are debtors (that's what debit/Dr used to mean) and on the RHS are creditors. This becomes obvious if you wind up the company, as used to be the practice after each business project/voyage ~1000 years ago in Italy. People on the RHS have given up some resources earlier and are due something, some more secured than others (seniority). If the LHS consists of real assets only, then the sole debtor is the agent running the company - he doesn't own the assets, just takes care of them for others (he might be one of the many shareholders, of course). The company is no one, and cannot thus really own anything either (it is fiction we have come up with in more modern times).
Anyway, wind up a central bank and you will find out that currency-/noteholders were due to receive something (as creditors)?
One problem with RHS/LHS is that I believe that balance sheet layouts can differ depending on language.
DeleteBut the division of the RHS (North American convention) into assets/liabilities can be contentious and changed depending upon context. National Accounts (SNA) lumps shareholder equity under "liabilities" (which gets some people mad).
But yes, the division of liabilities/equities is largely from the perspective of credit analysis - the equity bits are the first to go in a restructuring. Preferred shares get pushed into equity because management has the option of deferring payment - and the penalties of non-timely payment are just diluting equity. Preferreds cannot force a firm into bankruptcy (unless they have a really wacky structure). "Bank capital" is an attempt to reclassify various subordinated debt types as being "equity like."
Currency in circulation (although that might exclude coins) are a liability in that the private sector expects to be able to push them back to the central bank in exchange for transfers through the payment system/settlement balances ("reserves"). They are reserves in bearer form.
Since the central bank can't be forced into bankruptcy, the "liability-ness" of reserves seems vague. But they are certainly paid off if the central bank shrinks its balance sheet. Although one can argue that the central bank cannot be "forced" to shrink its balance sheet, if they act in too high-handed a fashion towards the domestic banking sector, that banking sector could start to fail and the private sector move towards using foreign currencies (or whatever).
Yes, notes (currency) are reserves in bearer form. Or I would say they are credit balances in bearer form, while reserves are credit balances on the ledger. I rather like Neil Wilson's suggestion (Substack) that we should talk about credits and debits, and forget liabilities/equity. (Only accountants can truly understand the monetary system, because it is all about accounting.)
DeleteSo, holding currency proves you are a creditor. What kind of creditor? Obviously not someone who can point out a debtor and demand repayment. In that sense it is not different from "equity credit balance". But you do hold a secured nominal claim against the debtors (debit balance holders) recorded in the CB ledger - again, just wind up the CB and you will find out. A debt is a debt, whether the creditor can force its repayment or not.
Coins are much like government bonds. That's why the Fed has the coins it holds recorded where it has Treasury bonds, too -- as a debit balance. Coins should logically be recorded as public debt. But are not? In the US:
"Because the Mint, a part of Treasury, is included in the budget, the
recognition of the earnings from coins—the difference between production
costs and face value, called seigniorage—is shown in the federal budget as a reduction in needed borrowing for the government, after the deficit or
surplus for the year is calculated." https://www.gao.gov/assets/gao-04-283.pdf (Recommended reading!)
(I considered replying on Substack, but didn't want to confuse other readers.)
It's not clear that coins are returned in practice to the government. In which case, they lose their "liability-ness."
DeleteGood post! I agree with your main argument.
ReplyDeleteA little quibble as an aside, if I may. While I agree that central banks, or the banking system as a whole, behave(s) differently if there is no promise of conversion into a real ressource, I'm not sure it's helpful to make the strong claim that 'Central banks in free-floating (“fiat”) currencies are special.' For one, and I think this is in line with what you're saying, the accounting is identical in either case. Secondly, the inflation option, and thus the inflation constraint, also applies to a convertible currency or metal coinage. 'Crying down' the currency or clipping or debasing coinage were all ways to circumvent liquidity contstraints by altering the official rate at which the unit of account translates into real ressources.
Similarly, I find the case for claiming that modern central banks are special viz. commercial bank to be weak. Accounting wise, it's all the same if one looks past the names given to the specific items (reserves, currency, checking accounts etc.). The only real difference is whom management is accountable to. I.e., who are the relevant stakeholders and what is the mandate?
So in all, I'd say by focussing on accounting, which to me is the only way to go, the secret sauce of central banks becomes less secret and less saucy and rather more generic instead. That's the beauty of it.
Central banks in free-floating currencies are special because they cannot be forced into insolvency/restructuring. Private banks certainly can, and countries with currency pegs can certainly be forced to default on their redemption ratio pledge - which is a default on legal obligations, and hence a restructuring. (A CB with a peg can structure its affairs to avoid bankruptcy - a currency board - but free-floating currency CB's are free of such constraints.)
DeleteRestructuring means management actively has to do something to avoid bankruptcy. But they can, so it's not as binding as you suggest. But anyway, if we can agree that equity is a type of credit (see Antti's comment above e.g.), then debiting the equity account to the point it becomes negative (negative entry on RHS) can just as well be thought of as having a positive entry on the LHS = debt. So allowing equity to go negative means equity holders consent to automatically becoming debtors. In certain circumstances this might be good policy for a government, at least up to a certain point. And while commercial banks could draw up similar contracts, most investors would not wish to hold such a product. But importantly, technically, i.e accounting-wise, pretty much everything is possible - accounting is only arithmetics, after all. Differences arise due to differing policy objectives/ mandates. If you're arguing from an accounting perspective, focusing on symmetries rather than differences is the right way to go, imo
DeleteA restructuring is literally a bankruptcy. A restructuring is when an entity failed to meet its contractual obligations, and the obligations are changed as part of allowing the entity to continue operation. A bankruptcy does not require liquidation.
DeleteI am unsure about the rest of your comments. If a central bank has a currency peg, not everything is possible - you have a hard constraint to convert your currency at a fixed rate, and once they run out of the backing instrument, they HAVE to default on the conversion pledge. No amount of accounting magic can make physical gold appear out of thin air.
My point is that floating currency central banks do not face such constraints.
I did indeed equate bankruptcy with liquidation. My bad.
DeleteThe case I had in mind was say the HKD peg to the USD. First off, if the currency board saw its forex reserves depleting, it could preemptively change the peg. Or, if it were challenged by the markets, it could do the same reactively. In either case, both gvt and cb liabilities, i.e. the contracts, are mostly denominated in the local currency, not the foreign currency it's pegged to. So no, you can't make gold appear, but you can renege on your promises regarding the exchange rate. It's just that the redenomination / devaluation is an official act, as opposed to being left to the market in a so-called free floating regime. Same applies to commodity standards. Would you call that restructuring? I'll grant you that the dynamics btw. managed and market led regimes may differ in times if crisis. But the accounting is much the same.
As for my comment on negative equity - before you put me on your quack list - I was merely pointing out that another word for a negative credit (or liability from the perspective of the bank) is a debt (or asset from the bank's perspective. While the term negative equity makes sense in terms of credit analysis, from the simple, binary 'accounting view' I'm arguing from (see Neil Wilson's comment re credits & debits), it's a bit like calling your overdraft balance negative money. Not wrong but unnecessarily convoluted.
1) A peg is a legal commitment to convert your currency to another instrument (foreign currency, gold) at a fixed rate. If you break the peg, you are reneging on a legal commitment, and this will have real world consequences on entities that conducted their affairs on the basis of the peg continuing. Even if courts rule a peg break to not be a default (UK had a case on this in the 1930s, I think) on government debt (although "gold clauses" existed in some debt contracts that had to be broken), there is still a rupture of a legal commitment that everybody is going to view as a restructuring of government affairs. It is easy to find people who are still mad about the gold peg changes by the U.S. in the 1930s (?) and the early 1970s.
DeleteCountries may have policy aspirations - like an inflation target, or vaguely-defined currency targets. In such a case, there is no good case to refer to changes as being a "default" or "restructuring". However, the lack of a peg with a legal commitment turns a currency into a floating fiat currency. To rephrase my original point: the lack of a legal hard financial constraint on the central bank is a feature only of central banks in free floats; every other type of bank (private/public) faces hard constraints that can lead to restructuring event (default on payments, peg break).
2) I do not understand your point about definitions. Central banks in fiat currencies can operate with negative equity, as I noted from the beginning. Banknotes (and settlement deposits at the central bank) act in a fashion that is indistinguishable from any other liability on the central bank's balance sheet, and the amounts involved are positive. (If a private bank runs an overdraft at the central bank, it should turn into an asset of the central bank. If that differs from actual practice would just be a quirk of bank accounting without any real world import since such overdrafts by private banks at the central bank have extremely limited volumes.)
Thanks for your patience and answer(s). You're saying pegs are legally enforceable commitments by the monetary authorities? I was under the impression that they were legally on par with such things as price level targets etc. but more binding in the sense of entailing a concrete number which private contracts could / would then reference. If not, I stand corrected. As for the second point, I see I haven't expressed myself clearly. One last attempt. Since equity is also a type of credit / liability, negative equity must logically be a deb(i)t / asset, meaning that the original equity holders become debtors. Just a preference for how to look at things, not an argument, really. Just wondering whether you might agree with it. Happy Christmas!
Delete1) There is a continuum. The "enforceability" is always questionable when dealing with the government (they can change the laws at any time). But some pegs were quite hard - gold Standard pegs with gold clauses in debt contracts. That said, it was always understood that gold pegs would be suspended in wartime. The Bretton Woods system was a creature of treaty law, not domestic laws. Some countries have "serious" pegs where the explicitly say they will defend a particular parity, while others have crawling pegs. It seems likely that central banks will start entering into currency peg arrangements on their own discretion, they would usually be mandated by law to enter into the arrangement. As such, there is a legal component to holding the peg.
DeleteIn any event, the central bank will only be able to continue operating by breaking that commitment to redeem their currency to the external instrument at the commitment rate. A floating currency sovereign has no such obligation, and so there is no commitment to point to that can be broken.
If a central bank says that it will not attempt to defend a peg, the peg is not credible and thus very vulnerable to a run. They therefore need to adjust policy to maintain the peg - which constrains their policy options.
2) Equity is the bottom of the seniority hierarchy, and only gets payment in a liquidation after senior creditors are paid out. (In practice, they can sometimes extract payments as a result of their ability to continue expensive litigation that destroys the value of the firm.) Meanwhile, if retained earnings are negative, the payment of dividends is normally suspended. This means that negative equity puts equity holders in an extremely bad economic position under the assumption that balance sheet valuations are economically meaningful.
Correspondingly, they do not really "turn into" debtors - they are always "debtors" in that they are stakeholders in a liquidation. All that happens is that the balance sheet says their stake is most likely worthless, and they would likely have lost their ability to receive dividends before equity even gets negative.
Assets = Liability + (Owner's/Shareholder's Equity). OE is a plug accounting term that keeps the two sides of the balance sheet in balance. Although one could write
Assets + ("-OE") = Liabilities
if OE is negative, it's not really worth re-writing accounting textbooks to deal with a situation that is not normally sustainable for most firms.
Happy Christmas!